New examples in the study of selectively separable spaces

The property of being selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fréchet-Urysohn, and we produce two additional examples from weaker assumptions.

Publication Details

Journal
ArXiv.org
Published
2025-09-26
Primary Topic
Genomics and Phylogenetic Studies
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article

New examples in the study of selectively separable spaces

ArXiv.org
Genomics and Phylogenetic Studies
article

New examples in the study of selectively separable spaces

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Abstract

The property of being selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fréchet-Urysohn, and we produce two additional examples from weaker assumptions.

ArXiv.org
Openalex Percentile: Top 49%
Genomics and Phylogenetic Studies
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New examples in the study of selectively separable spaces · ArXiv.org (2025) | TGRS Research Map | TGRS